# Reactor Design Economics

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This Demonstration calculates the monetary profit as a function of reactor volume for a continuous stirred-tank reactor (CSTR) or a plug-flow reactor (PFR). The reaction is either first-order or autocatalytic; set the feed concentrations of reactant and product with sliders. Use sliders to set the value of the product and the costs of the reactant and reactor. Select "concentration" to view the reactant and product concentrations plotted versus reactor volume. The final volume corresponds to the volume at the black dot on the profit plot. Click and drag the black dot on the profit versus reactor volume plot. Check "optimize" to solve for the reactor volume with the highest profit. The separations cost is not considered in this Demonstration, but it can significantly affect profit.

Contributed by: Rachael L. Baumann and Garrison J. Vigil (November 2015)
Additional contributions by: John L. Falconer, Nathan S. Nelson, and Nick Bongiardina
(University of Colorado Boulder, Department of Chemical and Biological Engineering)
Open content licensed under CC BY-NC-SA

## Details

The rate of reaction for a first-order reaction is given by:

,

and for an autocatalytic reaction it is:

,

where is the rate constant (1/min), and and are the reactant and product concentrations (mol/L).

A mass balance determines and for a continuous stirred-tank reactor (CSTR):

,

,

where is the reactor volume (L), is the inlet volumetric flow rate (L/s) and and are the reactant and product feed concentrations (mol/L).

For a plug-flow reactor (PFR):

,

.

Overall conversion of reactant to product and profit made are calculated:

;

for a CSTR:

,

for a PFR:

,

where ($/mol) and ($/[L min]) are the costs of the reactant and reactor and (\$/mol) is the value of the product.

## Permanent Citation

Rachael L. Baumann and Garrison J. Vigil

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